Gradient correction and Bohm potential for two‐ and one‐dimensional electron gases at a finite temperature

Moldabekov, Zhandos A.; Bönitz, M.; Рамазанов, Т. С.

doi:10.1002/ctpp.201700113

Cited by 32 publications

(14 citation statements)

References 38 publications

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“…For these low-dimensional configurations, the closure relations for the quantum pressure (Bohm potential) are fundamentally different from the 3D case, and the resulting dispersion relations are different too. These issues were discussed in a recent work [58].…”

Section: Discussionmentioning

confidence: 99%

Fluid descriptions of quantum plasmas

Manfredi¹,

Hervieux²,

Hurst³

2021

Preprint

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Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nanoscale objects. Compared to more standard approaches, such as density functional theory or phase-space methods based on Wigner functions, fluid models require the solution of a small number of equations in ordinary space, implying a lesser computational cost. They are therefore well suited to study systems composed of a very large number of particles, such as large metallic nanoobjects. They can be generalized to include the spin degrees of freedom, as well as semirelativistic effects such as the spin-orbit coupling. Here, we review the basic properties, advantages and limitations of quantum fluid models, and provide some examples of their applications.Keywords Solid-state plasmas • Quantum hydrodynamics • Vlasov and Wigner equations • Nanoplasmonics. Introduction -Fluid models for classical and quantum plasmasRecent decades have witnessed a remarkable surge of interest for the electronic properties of nano-scale objects, particularly when excited by electromagnetic radiation [11,53,54,78]. This is a very vast domain of research that encompasses

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Section: Discussionmentioning

confidence: 99%

Fluid descriptions of quantum plasmas

Manfredi¹,

Hervieux²,

Hurst³

2021

Preprint

View full text Add to dashboard Cite

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“…Also, we have [16]

σ = {italicie}^{2} n_{0} ω [\frac{1}{m_{e}} \frac{1}{ω^{2} - α q^{2}} + \frac{1}{m_{i}} \frac{1}{ω^{2}}],

where e is the element charge, m e ( m i ) is the electron (ion) mass,

α = v_{F}^{2} / 2

(that is square of the speed of propagation of the density disturbances in a 2D Fermi electron plasma) and v F = ℏ k F / m e and

k_{F} = \sqrt{2 π n_{0}}

are electron Fermi speed and electron Fermi wave number in the 2D electron plasma layer, respectively [17]. We note that the general form of Equation (6) contains the contribution of the quantum diffraction (quantum Bohm) effect [18,19]. However, as mentioned in Ref.…”

Section: Theorymentioning

confidence: 99%

Energy relations of plasma waves in planar two‐dimensional electron‐ion plasmas

Moradi

2020

Contributions to Plasma Physics

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A derivation of the energy densities and power flows of plasma waves in a planar two‐dimensional electron‐ion plasma is presented through a simple approach. In this method, the response of an external current density introduced into the system is determined by a so‐called dispersion function. The advantage of the dispersion function is that it yields not only the dispersion relations of both plasmon (high‐frequency) and ion‐acoustic (low‐frequency) waves of the system, but expressions for the energy relations as well.

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“…Based on the linearized QHD theory, the electronic excitations of the system can be described by the continuity equation

\partial_{t} n (x, t) + n_{e 0} \partial_{x} v_{x} (x, t) = 0,

and the momentum balance equation

\partial_{t} v_{x} (x, t) = \frac{e}{m_{e}} \partial_{x} Φ - \frac{α^{2}}{n_{normale 0}} \partial_{x} n (x, t) + γ \frac{β^{2}}{n_{normale 0}} \partial_{x} \partial_{italicxx} n (x, t),

where m e is the electron mass, and Φ is the self‐consistent potential. On the right‐hand side of Equation , the first term is the force on an electron due to the electric field, the second term is the quantum statistical effects, which is the force due to the internal interactions in the electron species, and the third term is the quantum diffraction effects coming from the quantum pressure.…”

Section: Dispersion Relation and Group Velocitymentioning

confidence: 99%

Propagation of electrostatic energy through a quantum plasma

Moradi

2018

Contributions to Plasma Physics

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The theory of propagation of electrostatic energy through an infinite, homogeneous electron-ion quantum plasma is presented. Simple expressions for the energy flow, energy density, and energy velocity of longitudinal oscillation waves in the system are derived using the linearized quantum hydrodynamic theory for the electron fluid, which incorporates the important quantum statistical pressure and electron diffraction force, while the optical response of the ion particles is characterized by the classical frequency-dependent dielectric function, ion . Both cases of plasmon (high-frequency) and quantum ion-acoustic (low-frequency) waves are considered. KEYWORDSelectrostatic wave, energy density, energy flow, quantum plasma 1

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Gradient correction and Bohm potential for two‐ and one‐dimensional electron gases at a finite temperature

Cited by 32 publications

References 38 publications

Fluid descriptions of quantum plasmas

Fluid descriptions of quantum plasmas

Energy relations of plasma waves in planar two‐dimensional electron‐ion plasmas

Propagation of electrostatic energy through a quantum plasma

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